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Abstract

Metal-helix based metamaterials have been introduced as compact and broadband circular
polarizers. However, the end of the metal wire together with the helix center defines an axis
in space, which unavoidably breaks the rotational symmetry at the metamaterial surface. This
introduces linear birefringence. Symmetry can be recovered by considering an integer number,
e.g. N = 4, of intertwined helices arranged to a square array. We show that
the operation principles are fundamentally different though. Metamaterial circular polarizers
based on N = 4 helices, unlike single helices, inherently require absorption
of the constituent metal. Otherwise, the combination of a four-fold rotational axis and
time-inversion symmetry strictly forbids circular-polarizer action. Our symmetry analysis is
confirmed by extensive numerical calculations comparing results for perfect electric conductors
with those for a free-electron Drude metal with finite damping.

Figures (3)

Illustration of the unit cells of helix-metamaterial geometries
considered in this work. In each case, top view (left) and oblique view (right) are depicted.
(a) Single (N = 1) left-handed metal helices with axial period
a arranged to a square array with lateral lattice constant
a. The metal wire diameter is d=0.1×a, the helix diameter is D=0.6×a. Note that the end of the metal wire together with the center
axis of the helices defines an axis in space. This leads to a one-fold rotational axis. (b)
Similarly arranged N = 4 intertwined helices recover a four-fold rotational
axis compatible with the square-array symmetry. (c) Arrangement of single helices like in (a)
effectively recovering four-fold rotational symmetry of the overall structure by laterally
displacing the four helices from (b) within one new unit cell with lattice constant
2a.

Calculated normal-incidence intensity transmittance (solid), reflectance (solid), and conversion spectra (dashed). Incident left-handed circular polarization (LCP) is shown in red, incident right-handed circular polarization (RCP) in blue. In cases where no blue curve is visible, the blue curve is identical to the red one to within the curve linewidth. The left-handed N = 1 (left column, i.e., (a) and (c)) and N = 4 (right column, i.e., (b) and (d)) structures are defined in Fig. 1(a) and Fig. 1(b), respectively. The insets at the top repeat the top view onto a unit cell. For the top row of the overall 2×2 matrix (i.e., (a) and (b)), the metal is treated as a lossless perfect electric conductor (PEC), for the bottom row (i.e., (c) and (d)) as a free-electron Drude model with finite damping/losses (gold parameters).

As Fig. 2(d), but for more than one helix pitch along the helix axis as indicated. (a) same as Fig. 2(d) with 1 pitch, (b) 2 pitches, (c) 3 pitches, and (d) 6 pitches. Note that all conversions (dashed) are strictly zero. In reflection, no blue solid curves are visible because they are identical to the red ones to within the curve linewidth. The equal gray areas in (a)-(d) highlight the frequency interval for which broadband circular-polarizer action is observed for several axial pitches.